Evolution is not
only the development of new species from older ones, as most people assume.
It is also the minor changes within a species from generation to generation
over long periods of time that can result in the gradual transition to new
species.

The biological sciences now
generally define evolution as being the sum total of the genetically inherited
changes in the individuals who are the members of a population's gene pool. It
is clear that the effects of evolution are felt by individuals, but it is the population
as a whole that actually evolves. Evolution is simply
a change in frequencies of alleles in the
gene pool
of a population. For instance, let
us assume that there is a trait that is determined by the inheritance of
a gene with two alleles--B and
b.
If the parent generation has 92% B and
8% b and
their offspring collectively have 90% B and 10%
b,
evolution has occurred between the generations. The entire population's
gene pool has evolved in the direction of a higher
frequency of the b
allele--it was not just those individuals who inherited the
b
allele who evolved.

Godfrey
Hardy
(1877-1947)

Wilhelm Weinberg
(1862-1937)

This definition of evolution
was developed largely as a result of independent work in the early 20th century by
Godfrey
Hardy, an English mathematician, and Wilhelm Weinberg, a German physician. Through
mathematical modeling based on probability, they concluded in 1908 that gene pool frequencies are inherently stable but
that evolution should be expected in all populations virtually all of the time. They
resolved this apparent paradox by analyzing the net effects of
potential evolutionary
mechanisms.

Hardy, Weinberg, and the
population geneticists who followed them came to understand that evolution will not occur
in a population if seven conditions are met:

These conditions are the absence of
the things that can cause evolution. In other words, if no
mechanisms of evolution
are acting on a population, evolution will not occur--the gene pool
frequencies will remain unchanged. However, since it is highly unlikely
that any of these seven conditions, let alone all of them, will
happen in the
real world, evolution is the inevitable result.

Godfrey Hardy and
Wilhelm Weinberg went on to develop a
simple equation that can be used to discover the
probablegenotype frequencies in
a population and to track their changes from one generation to another.
This has become known as the Hardy-Weinberg
equilibrium equation.In
this equation (p² + 2pq + q² = 1),
p is defined as the frequency of the dominant
allele and q as the frequency of the recessive
allele for a trait controlled by a pair of alleles (A and
a). In other
words, p equals all of the alleles in
individuals who are homozygous
dominant (AA) and half of the alleles in people who are
heterozygous (Aa) for this trait
in a population.
In mathematical terms, this is

p = AA + ½Aa

Likewise, q
equals all of the alleles in individuals who are homozygous recessive (aa)
and the other half of the alleles in people who are heterozygous (Aa).

q = aa + ½Aa

Because there are only two alleles
in this case, the frequency of one plus the frequency of the other must equal 100%, which
is to say

p + q =
1

Since this is logically true, then the following must also be
correct:

p = 1 - q

There were only a few short steps
from this knowledge for Hardy and Weinberg to realize that the chances of all possible
combinations of alleles occurring randomly is

(p + q)² = 1

or more simply

p² + 2pq + q² = 1

In this
equation, p² is the predicted frequency of homozygous dominant (AA)
people in a population,2pq is the
predicted
frequency of heterozygous (Aa) people, and q² is the
predicted frequency of homozygous recessive (aa)
ones.

From observations of phenotypes, it is usually only possible to know the
frequency of homozygous recessive people, or q² in the
equation, since they will not have the dominant trait. Those who express the trait in their
phenotype could be either homozygous dominant (p²)
or
heterozygous (2pq). The Hardy-Weinberg equation allows us
to predict which ones they are. Since p = 1 - q
and q is known, it is possible to calculate p as well. Knowing p and q, it is a simple matter to plug these values into the
Hardy-Weinberg equation (p² + 2pq + q² = 1).
This then provides the predicted frequencies of all three genotypes for the selected trait
within the population.

By comparing genotype frequencies from the next generation
with those of the current generation in a population, one can also
learn whether or not evolution has occurred and in what direction and rate for the
selected trait. However, the Hardy-Weinberg equation cannot determine which of the
various possible causes of evolution were responsible for the changes in gene pool
frequencies.

Significance of the
Hardy-Weinberg Equation

By the outset of the 20th century,
geneticists were able to use Punnett
squares to predict the probability of offspring genotypes for particular
traits based on the known genotypes of their two parents when the traits
followed simple Mendelian rules of dominance and recessiveness. The
Hardy-Weinberg equation essentially allowed geneticists to do the same thing
for entire populations.

It is important not to lose
sight of the fact that gene pool frequencies are inherently stable. That is to say,
they do not change by themselves. Despite the fact that evolution is a common
occurrence in natural populations, allele frequencies will remain
unaltered indefinitely
unless evolutionary mechanisms such as mutation and natural selection
cause them to change. Before Hardy and Weinberg, it
was thought that dominant alleles must, over time, inevitably swamp
recessive alleles out of existence. This incorrect theory was called
"genophagy" (literally "gene eating"). According to this
wrong
idea, dominant alleles always increase in frequency from generation to
generation.
Hardy and Weinberg were able to demonstrate with their equation that
dominant alleles can just as easily decrease in frequency.

The next six sections of this tutorial
explore the mechanisms in nature that
cancause evolution to occur.